Improved accuracy estimation of the Tikhonov method for ill-posed optimization problems in Hilbert space

DOI10.1134/s0965542523040103OpenAlexW4378676677MaRDI QIDQ6159046

Mikhail M. Kokurin

Publication date: 1 June 2023

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542523040103

zbMATH Keywords

Tikhonov methodaccuracy estimationill-posed optimization problem in Hilbert space

Mathematics Subject Classification ID

Numerical analysis (65-XX) Operations research, mathematical programming (90-XX)

Cites Work

• Unnamed Item
• Regularization methods in Banach spaces.
• Necessary and sufficient conditions for power convergence rate of approximations in Tikhonov's scheme for solving ill-posed optimization problems
• Source conditions and accuracy estimates in Tikhonov's scheme of solving ill-posed nonconvex optimization problems
• Convergence rate estimates for Tikhonov's scheme as applied to ill-posed nonconvex optimization problems
• A global minimization algorithm for Tikhonov functionals with $p-$convex ($p\,\geqslant \,2$) penalty terms in Banach spaces
• On the method of Lavrentiev regularization for nonlinear ill-posed problems
• Morozov's discrepancy principle for Tikhonov-type functionals with nonlinear operators

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